“I was just called by the head people at Sprint, and they are going to be bringing 5,000 jobs back to the United States,” Mr. Trump told reporters at his Mar-a-Lago estate in Florida. “They have taken them from other countries. They are bringing them back to the United States.”

Although Mr. Trump claimed credit for SoftBank’s $50 billion investment in the United States, those plans predated the election, and Mr. Son has owned a controlling stake in Sprint, among other companies, for several years.

A Sprint spokeswoman, Adrienne Norton, said that the 5,000 jobs are part of the 50,000 increase Mr. Son promised, but that the new positions would be financed by the mobile phone carrier. “It will be a combination of newly created jobs and bringing some existing jobs back to the U.S.,” she said.

Since the election, Sprint shares have risen nearly 40 percent, partly on hopes that it could be acquired by its rival T-Mobile. While antitrust officials under President Obama have been wary of deals in the telecom sector, Mr. Son and investors are hoping the Trump administration might look more favorably on any potential deal.

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In January, as part of a restructuring effort, Sprint cut 2,500 jobs in call centers across the United States and at its headquarters in Overland Park, Kan.

On Wednesday, the company said in a statement that it would be creating or bringing back jobs in a variety of departments, including customer care and sales, and that all would be added by the end of its 2017 fiscal year. It was not clear where in the country those jobs would be.

“We are excited to work with President-elect Trump and his administration to do our part to drive economic growth and create jobs in the U.S.,” said Marcelo Claure, Sprint’s chief executive.

In November, Mr. Trump reached a deal with Carrier to keep roughly 850 jobs at its factory in Indianapolis instead of shifting them to Mexico, which the company said it would do in February. Despite Mr. Trump’s pressure, Carrier and its parent, United Technologies, still plan to move more than 1,000 jobs now in Indiana to Monterrey, Mexico.

They are not the only ones. Another Indianapolis factory, owned by the ball bearing maker Rexnord, also plans to soon leave Indianapolis for Mexico, despite criticism from the president-elect on Twitter and threats to impose steep tariffs on companies that move production abroad.

Correction: December 30, 2016

A web summary with an earlier version of this article referred incorrectly to SoftBank. It is a technology conglomerate, not a bank.

A version of this article appears in print on December 29, 2016, on Page A16 of the New York edition with the headline: Trump Takes Credit in Plan by Sprint for Jobs in U.S. Order Reprints|Today's Paper|Subscribe